Digital communication requires the transmission of data symbols. For frequency modulation (FM), each symbol defines a change in the frequency of the transmitted signal or, as indicated in FIG. 1 to which reference is now made, as a set of changes in the frequency.
FIG. 1 shows two Manchester encoded bits. When using FM, a "1" bit has the frequency of .function..sub.0 +.DELTA..function. during the first T/2 seconds (from t.sub.0 to t.sub.1 of FIG. 1) of the bit and the frequency of .function..sub.0 -.DELTA..function. during the second T/2 seconds (from t.sub.1 to t.sub.2) of the bit. A "0" bit has the opposite shape: during the first T/2 seconds (from t.sub.2 to t.sub.3) of the bit the frequency is .function..sub.0 -.DELTA..function. and during the second T/2 seconds (from t.sub.3 to t.sub.4) of the bit the frequency is .function..sub.0 +.DELTA..function.. For advanced mobile phone service (AMPS) wideband data transmission, the bit duration T is 0.1 msec (i.e. bit rate is 10 KHz) and .DELTA..function. is 8 KHz.
Attempts have been made to decode the symbol values using the in-phase i(t) and quadrature q(t) components of the baseband version of the complex transmitted signal, where:
i(t)=A cos(2.pi.ft+.theta.), EQU q(t)=A sin(2.pi.ft+.theta.)tm Equation 1
where f is the instantaneous frequency+.DELTA..function. or -.DELTA..function. of the baseband signal and .theta. is the instantaneous phase of the baseband signal.
FIG. 2, to which reference is now made, illustrates a unit circle 14 within an i-q coordinate system and the movement of the signal of FIG. 1 along circle 14. At the beginning (t.sub.0), the signal of FIG. 1 has a first phase .eta..sub.0, shown in FIG. 2 as somewhere within quadrant I.
When the frequency is +.DELTA..function., the signal moves counter clockwise along the circle 14 and when the frequency is -.DELTA..function., the signal moves clockwise along the circle 14. Thus, during the first portion of the 1 bit, the signal moves counter clockwise along the circle 14 until it reaches the position indicated by t.sub.1. In this example, t.sub.1 is in quadrant II. During the second portion of the 1 bit, the signal moves clockwise, arriving, at time t.sub.2, to a position close, if not equal to, the position at time t.sub.0. During the first portion of the 0 bit, the signal moves clockwise, moving to quadrant IV by time t.sub.3 and then, during the second portion of the 0 bit, the signal moves counter clockwise back to a position close, if not equal to, the position at time t.sub.2.
U.S. Pat. No. 4,322,851 to Vance describes a decoder which utilizes the in-phase and quadrature information to decode binary FSK bits. U.S. Pat. No. 5,469,112 to Lee describes a decoder which also utilizes the in-phase and quadrature information but to decode multi-level FSK bits. Neither of U.S. Pat. No. 4,322,851 or U.S. Pat. No. 5,469,112 will successfully decode general FM modulated symbols (e.g. Manchester encoded bits) since both assume that each has a constant value.